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Please help me now urgent 93 Show that any positive odd integer is of the form 8q + 1 or 8q + 3 or 8q + 5 or 8q + 7 where q is some integer. [CBSE 2012]

Correction in 4th step.

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let a be any positive integer
and b=8
By EUCLID'S DIVISION ALGORITHM,
a=bq+r
so a=8q+0
      a=8q
    a=2(4q)
SINCE 2 IS A FACTOR OF THE ABOVE NUMBER ITS AN EVEN NUMBER
  2ND CASE:
a=8q+1
SINCE 8q IS EVEN WHICH IS PROVED FROM ABOVE, THEN WE KNOW THAT:
EVEN NUMBER+1==ODD NUMBER 
Hence a=8q+1 is ODD
3RD CASE 
a=8q+2
a=2(4q+1)
SINCE 2 IS A FACTOR OF THE NUMBER ITS CONSIDERED EVEN 
4TH CASE
a=8q+3
a=8q+2+1
a=(8q+2)+1
SINCE 8q IS EVEN WHICH IS PROVED FROM ABOVE, THEN WE KNOW THAT:
EVEN NUMBER+1==ODD NUMBER 
SINCE 2 IS A FACTOR OF THE NUMBER ITS CONSIDERED EVEN 
4TH CASE 
a=8q+4
a=2(4q+2)
SINCE 2 IS A FACTOR OF THE NUMBER ITS CONSIDERED EVEN.
5TH CASE 
a=8q+5
a=8q+4+1
a=(8q+4)+1
SINCE 8q+4 IS EVEN WHICH IS PROVED FROM ABOVE, THEN WE KNOW THAT:
EVEN NUMBER+1==ODD NUMBER